Question 1

Which of the following is the correct simplification of $$\sqrt{-36}$$?

Accepted Answer

$$6i$$

Question 2

Given the complex numbers $$z_1 = 3 - 6i$ and z_2$ = -7 + 4i$$, what is $$z_1$$ + $$z_2$$?

Accepted Answer

$$-4 - 2i$$

Question 3

What is the product $$(1 - 2i)(1 + 2i)$$?

Accepted Answer

$$5$$

Question 4

Which of the following is the conjugate of $$-8 - 5i$$?

Accepted Answer

$$-8 + 5i$$

Question 5

Simplify $$i^{127}.$$

Accepted Answer

$$i$$

Question 6

Which of the following is a quadratic function?

Accepted Answer

$$f(x) = -3x^2$ + 2x + 1$$

Question 7

Solve the equation $$(x + 2)(2x - 1) = 0.$$

Accepted Answer

$$x = -2 or$$ $$x = \frac{1}{2}$$

Question 8

What is the solution to $$2(x + 3)^2$ + 1 = 9$$?

Accepted Answer

$$x = -3 \pm 2$$

Question 9

Which formula is used to find the solutions to $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 10

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what can you conclude about the solutions?

Accepted Answer

There are two different imaginary number solutions.

Question 11

A box is made from a $$10	ext{ cm} 	imes 20	ext{ cm}$$ piece of tin by cutting squares from each corner and folding up the sides. If the area of the base is $$96	ext{ cm}^2$$, what is the length $$x of $$the removed square?

Accepted Answer

$$x = 2$$

Question 12

Given $$f(x) = 3x^2$ - 6x + 1$$, what is the vertex form of the function?

Accepted Answer

$$f(x) = 3(x - 1)^2$ - 2$$

Question 13

For the quadratic function $$f(x) = -16x^2$ + 48x + 2$$, what is the maximum value?

Accepted Answer

$$38$$

Question 14

Solve the rational equation $$\frac{x}{x+1} = \frac{3}{2(x-1)}$$ for $$x ($$excluding extraneous solutions).

Accepted Answer

$$x = -3$$

Question 15

Solve the radical equation $$\sqrt{7 + x} - 5 = x.$$

Accepted Answer

$$x = 2$$

Question 16

Solve the absolute value equation $$|3x - 4| + 7 = 12.$$

Accepted Answer

$$x = \frac{11}{3} or$$ $$x = -1$$

Question 17

Which of the following describes the graph of $$f(x) = a(x-h)^2$ + k if$$ $$a \u003c 0$$?

Accepted Answer

The parabola opens downward.

Question 18

If $$|x - 5| \geq 3$$, what is the solution set?

Accepted Answer

$$x \leq 2 or$$ $$x \geq 8$$

Question 19

A baseball is hit 2 feet above the ground with an initial upward velocity of 48 ft/s. The height is given by $$s(t) = -16t^2$ + 48t + 2. At $$what time does the ball reach its maximum height?

Accepted Answer

$$t = 1.5$$ seconds

Quadratic Functions, Equations, and Inequalities: Study Notes for College Algebra (Precalculus)

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